Question

What is the math behind upper and lower indices used when studying representations of $\mathrm{SU}(N)$?

score 129 · Answer 1 · 2026-04-11 14:24:23

129

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What is the math behind upper and lower indices used when studying representations of $\mathrm{SU}(N)$?

Published on 11 Apr 2026 - 14:24

score 61 · Answer 2 · 2023-10-14 19:42:22

61

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Prove that the lie algebra $\mathfrak{so}(3)$ does not admit any two-dimensional Lie subalgebra.

Published on 14 Oct 2023 - 19:42

score 88 · Answer 3 · 2026-04-13 08:34:26

88

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Why (anti-)symmetric tensors are important in reducing the tensor product of representations of su($N$) and so($N$)?

Published on 13 Apr 2026 - 8:34

score 61 · Answer 4 · 2026-04-12 22:45:13

61

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Let $G$ be the group defined by $G = \{A \in \mathrm{GL}(2,\Bbb R) \mid A^tA=r^2I, r>0,\det A >0\}.$ Find the Lie algebra of $G$.

Published on 12 Apr 2026 - 22:45

score 167 · Answer 5 · 2026-04-12 19:28:54

167

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Weights of a representation of a semisimple Lie algebra

Published on 12 Apr 2026 - 19:28

score 100 · Answer 6 · 2026-04-12 20:19:35

100

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Real Lie subalgebras of o(3,1)

Published on 12 Apr 2026 - 20:19

score 39 · Answer 7 · 2023-10-20 03:19:37

39

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Universal enveloping algebra of an ideal of a Lie algebra

Published on 20 Oct 2023 - 3:19

score 53 · Answer 8 · 2026-03-25 22:25:08

53

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Convergence of Lie Series

Published on 25 Mar 2026 - 22:25

score 42 · Answer 9 · 2026-04-10 12:31:54

42

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Explicitly computing the complexification of Lie Algebras.

Published on 10 Apr 2026 - 12:31

score 71 · Answer 10 · 2026-04-12 23:15:49

71

Views

Determining whether an operator has maximal rank

Published on 12 Apr 2026 - 23:15

score 93 · Answer 11 · 2026-04-12 12:48:40

93

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Writing 1-parameter group of transformations as a composition of commutative 1-parameter transformations

Published on 12 Apr 2026 - 12:48

score 100 · Answer 12 · 2026-04-12 19:44:15

100

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Constructing Lie group from Lie algebra

Published on 12 Apr 2026 - 19:44

score 140 · Answer 13 · 2026-04-13 08:09:33

140

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Intuition behind the relationship between conjugation on a Lie group and the Lie bracket

Published on 13 Apr 2026 - 8:09

score 54 · Answer 14 · 2026-04-11 18:54:02

54

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About Reductive Lie Algebra

Published on 11 Apr 2026 - 18:54

score 60 · Answer 15 · 2023-10-23 19:20:27

Find the centers of $SU_{n}$, $SO_{n}(\mathbb{R})$ and $SL_{n}(\mathbb{C})$ and find all the connected lie groups certian the tangent algebras.

List Question

What is the math behind upper and lower indices used when studying representations of $\mathrm{SU}(N)$?

Prove that the lie algebra $\mathfrak{so}(3)$ does not admit any two-dimensional Lie subalgebra.

Why (anti-)symmetric tensors are important in reducing the tensor product of representations of su($N$) and so($N$)?

Let $G$ be the group defined by $G = \{A \in \mathrm{GL}(2,\Bbb R) \mid A^tA=r^2I, r>0,\det A >0\}.$ Find the Lie algebra of $G$.

Weights of a representation of a semisimple Lie algebra

Real Lie subalgebras of o(3,1)

Universal enveloping algebra of an ideal of a Lie algebra

Convergence of Lie Series

Explicitly computing the complexification of Lie Algebras.

Determining whether an operator has maximal rank

Writing 1-parameter group of transformations as a composition of commutative 1-parameter transformations

Constructing Lie group from Lie algebra

Intuition behind the relationship between conjugation on a Lie group and the Lie bracket

About Reductive Lie Algebra

Find the centers of $SU_{n}$, $SO_{n}(\mathbb{R})$ and $SL_{n}(\mathbb{C})$ and find all the connected lie groups certian the tangent algebras.

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